Summary

Appendixes

Source: http://www.abarim-publications.com/KochProof.html

Koch's snowflake or Koch's triangle

— Proof of infinite circumference and limited surface —

Helge von Koch's Snowflake or Triangle

Koch's Snowflakea.k.a.Koch's TriangleHelge von Koch

In 1904 the Swedish mathematician Helge von Koch created a work of art that became known as Koch's Snowflake or Koch's Triangle. It's formed from a base or parent triangle, from which sides grow smaller triangles, and so ad infinitum. That means that the circumference of Koch's Snowflake or Koch's Triangle keeps getting larger until infinity, while the surface it surrounds stays well within the order of magnitude of the parent triangle.

Fellow mathematicians and philosophers alike objected to such a paradox, but no amount of objections could make it ever go away. The Koch Concoction was there to stay. And proving that indeed the circumference is infinite, while the surface stays finite, isn't a big deal either: